I have been having a problem adding a paypal shortcode (tried 3 different plugins) when I have the tablepress shortcode on page. Have no idea what might be causing this, so I created a post with nothing on it except the shortcode for the table, and the shortcode for the paypal. Without tablepress, the button appears, with tablepress it still appears as a shortcode.

To be honest, I have no idea what could be causing this.
Therefore, if possible, I'd like to take a direct look at this on your site. For that, could you please create a temporary admin account for me to your site, and send me an email? The address is in the main plugin file "tablepress.php".

However, I could also reproduce it with the TablePress Shortcode removed from the page, and even with TablePress deactivated.
Due to that, I'm quite sure that TablePress has nothing to do with this problem. (The other reason for this assumption is that TablePress does not influence other plugin's Shortcodes.)

The reason must be in another plugin, or in the theme.
I recommend to turn off the caching during the debug process (deactivating WP-Super Cache is not enough for that, as clearing the cache also is not really working at the moment), and then turn off other plugins one by one, until the plain Shortcode for the PayPal button works.